Boat travels 10 mi upstream and 10 mi downstream the stream is moving 1mph and the boat took 5 1/3hrs. What is the speed of boat if the stream still?
Distance/time = rate
Let x = speed of boat (rate)
20/(16/3) = (x+1) + (x-1)
Assuming your data is correct, solve for x.
Rita paddles her canoe upstream at an average speed of 2 miles per hour and downstream at a rate of 3 miles per hour. find Rita's speed in still water and the speed of the river current.
To find the speed of the boat in still water, we need to use the concept of relative speed. Relative speed is the difference between the speed of an object and the speed of another object or the surrounding medium.
Let's break the problem down into steps:
1. We know that the boat traveled 10 miles upstream and 10 miles downstream. Since the stream is moving at a speed of 1 mph, the boat's effective speed will either be increased or decreased depending on the direction it is traveling.
2. Let's assume the speed of the boat in still water is 'x' mph.
3. When the boat is traveling upstream, against the stream, its effective speed will be reduced by the speed of the stream. So, the boat's speed becomes (x - 1) mph.
4. When the boat is traveling downstream, with the stream, its effective speed will be increased by the speed of the stream. So, the boat's speed becomes (x + 1) mph.
5. According to the problem, the boat took 5 1/3 hours to travel 10 miles upstream and 10 miles downstream.
Now, we can set up an equation using the formula:
Time = Distance / Speed.
For the upstream journey:
10 miles / (x - 1) mph = Time taken to travel upstream
For the downstream journey:
10 miles / (x + 1) mph = Time taken to travel downstream
Since the total time for both journeys is given as 5 1/3 hours, we can set up the following equation:
5 1/3 hours = Time taken to travel upstream + Time taken to travel downstream
Now, let's solve the equation step by step:
First, we convert 5 1/3 hours into an improper fraction:
5 1/3 = (3*5 + 1) / 3 = 16/3
The equation becomes:
16/3 = 10 / (x - 1) + 10 / (x + 1)
To simplify this equation, let's find the least common denominator (LCD). In this case, it is (x - 1)(x + 1):
16/3 = (10 * (x + 1) + 10 * (x - 1)) / [(x + 1)(x - 1)]
Simplifying further:
16/3 = (10x + 10 + 10x - 10) / [(x + 1)(x - 1)]
16/3 = (20x) / [(x + 1)(x - 1)]
Cross-multiplying, we get:
48(x + 1)(x - 1) = 20x
Expanding the brackets on the left side:
48(x^2 - 1) = 20x
Simplifying:
48x^2 - 48 = 20x
Rearranging the equation:
48x^2 - 20x - 48 = 0
Factoring the quadratic equation, we get:
4x^2 - 5x - 12 = 0
Solving this quadratic equation, we get two possible solutions for 'x' as:
x = 3
x = -4/3
Since the speed cannot be negative in this context, the speed of the boat in still water is 3 mph.
So, the speed of the boat in still water is 3 mph.